CN106874545B - Design method of flat plate with holes - Google Patents
Design method of flat plate with holes Download PDFInfo
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Abstract
The invention discloses a design method of a flat plate with holes, and belongs to the technical field of mechanical structure design. The method comprises constructing an initialized geometric model of the flat plate, generating a geometric mid-plane model of the flat plate according to the initialized geometric model, dispersing the geometric mid-plane model by using a finite element method, to obtain a mesh model, obtain the numerical value of the arc into which the initial circular hole is divided, obtain the material property and the material thickness, obtain the boundary condition of the flat plate, obtain the optimization design variable and the optimization target to obtain a shape optimization model, solve the shape optimization model, by obtaining the numerical value of the arc divided by the initial round hole, and obtaining the boundary condition, the optimization design variable, the optimization constraint condition and the optimization target to carry out optimization, and continuously adjusting the radius and the position of the arc divided by each section of the initial circular hole in the optimization process, and finally determining the shape and the position of the optimal hole meeting the optimization constraint condition and the optimization target to obtain an optimal shape model.
Description
Technical Field
The invention relates to the technical field of mechanical structure design, in particular to a design method of a flat plate with holes.
Background
Perforated plate structures are found in various mechanical devices, and are often used to support shafts, support various beams, or reduce weight by making holes in the plate.
The design of the perforated plate is important because after the plate is perforated, in actual operation, a large stress is generated near the hole, which may cause local material yield of the plate, thereby affecting the normal operation of the whole equipment. When an existing perforated flat plate is designed, an initialized geometric model of the flat plate is generally established according to experience or perforated flat plates in equipment with similar structure, then the structural performance of the initialized geometric model is checked, if the checking result meets the requirement of actual work, the initialized geometric model is determined as a final flat plate model, if the checking result does not meet the requirement of the actual work, the initialized geometric model of the flat plate needs to be established again according to experience again, and checking is carried out again until the checking result meets the requirement of the actual work.
Because the initial geometric model of the flat plate is established according to the flat plate with holes in equipment with similar experience or analog structures, the selection of the shapes, the positions and the sizes of the holes has certain blindness, so that repeated checking and redesigning are probably needed in the process of designing the flat plate with the holes, the design period is very long, and the design efficiency is low.
Disclosure of Invention
In order to solve the problems that the existing perforated flat plate is long in design period and low in design efficiency, the embodiment of the invention provides a design method of a perforated flat plate. The technical scheme is as follows:
a method of designing a perforated flat sheet, the method comprising:
constructing an initialized geometric model of the flat plate, wherein the initialized geometric model is provided with an initial round hole;
generating a geometric mid-plane model of the flat plate according to the initialized geometric model;
dispersing the geometric mid-plane model by adopting a finite element method to obtain a grid model;
acquiring the quantity value of the arc into which the initial round hole is divided;
acquiring material properties and material thickness;
acquiring the boundary condition of the flat plate;
obtaining an optimization design variable and an optimization target to obtain a shape optimization model;
solving the shape optimization model to obtain an optimal shape model with an optimal hole,
when a circular hole for supporting a rotating shaft or a circular-section beam is designed on the flat plate, the number of arcs into which the initial circular hole is divided is 1, the optimized design variable is the radius of the arcs,
when waist-shaped holes for weight reduction are designed on the flat plate, the number of arcs into which the initial circular hole is divided is 4, the optimized design variables are the radius of four segments of the arcs, the central angle of the four segments of the arcs and the distance from the centers of the four segments of the arcs to the position of the center of the initial circular hole,
when the waist-shaped holes for the support beams are designed on the flat plate, the number of the arcs into which the initial circular holes are divided is 4, and the optimized design variables are the radius of the four segments of the arcs, the central angle of the four segments of the arcs and the distance between the centers of the four segments of the arcs and the position of the center of the initial circular hole.
Preferably, the initializing geometric model of the flat plate comprises:
obtaining design parameters of the flat plate;
and generating the initialized geometric model according to the design parameters.
Further, the design parameters include the size of the flat plate, the center of the initial circular hole, and the radius of the initial circular hole.
Preferably, the generating a geometric mid-plane model of the flat panel according to the initialized geometric model includes:
and extracting the middle surface of the initialized geometric model to obtain the geometric middle surface model.
Further, the material properties include density, modulus of elasticity, and poisson's ratio.
Optionally, the boundary conditions include the degree of freedom of the slab and the maximum load experienced.
Optionally, the optimization objective is set according to performance requirements including at least one of structural stiffness, structural strength, natural frequency, volume and weight of the flat panel.
The technical scheme provided by the embodiment of the invention has the following beneficial effects: the size of the flat plate and the position of the circle center of the initial circular hole can be determined by establishing an initial geometric model of the flat plate, then the quantity value of arcs into which the initial circular hole is divided is obtained after generating a geometric middle model and a grid model of the flat plate, and the boundary condition, the optimized design variable and the optimized target are obtained for optimization, the radius of the arc into which each section of the initial circular hole is divided and the position of the circle center of the corresponding initial circular hole are continuously adjusted in the optimization process according to the boundary condition, the optimized design variable and the optimized target, and finally the shape and the position of the optimal hole meeting the boundary condition and the optimized target are determined to obtain an optimal shape model, and the perforated flat plate meeting the actual working requirements can be rapidly and accurately designed due to the optimization according to the boundary condition, the optimized design variable and the optimized target, so that the design period of the traditional design method is long, the design efficiency is low.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow chart of a method for designing a perforated plate according to an embodiment of the present invention;
FIG. 2 is a flow chart of another method for designing a perforated plate according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating an initialized geometric model of a flat panel according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a geometric mid-plane model provided by an embodiment of the invention;
FIG. 5 is a schematic diagram of a mesh model provided by an embodiment of the invention;
FIG. 6 is a schematic diagram of a plate with boundary conditions applied thereto according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of an optimal shape model provided by an embodiment of the invention;
FIG. 8 is a flow chart of another method for designing a perforated plate according to an embodiment of the present invention;
FIG. 9 is a schematic view of the initial circular hole after segmentation;
FIG. 10 is a schematic diagram of a plate with boundary conditions applied thereto according to an embodiment of the present invention;
FIG. 11 is a schematic diagram of an optimal shape model provided by an embodiment of the invention;
FIG. 12 is a flow chart of a method for designing a perforated plate according to an embodiment of the present invention;
FIG. 13 is a schematic view of the initial circular hole after segmentation;
FIG. 14 is a schematic diagram of another plate with boundary conditions applied thereto according to an embodiment of the present invention;
fig. 15 is a schematic diagram of an optimal shape model according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
Fig. 1 is a flow chart of a method for designing a perforated flat plate according to an embodiment of the present invention, as shown in fig. 1, the method includes:
s11: and constructing an initialized geometric model of the flat plate, wherein the initialized geometric model is provided with an initial round hole.
S12: and generating a geometric mid-plane model of the flat plate according to the initialized geometric model.
S13: and (4) dispersing the geometric mid-plane model by adopting a finite element method to obtain a grid model.
S14: the numerical value of the arc into which the initial circular hole is divided is obtained.
S15: and acquiring material properties and material thickness.
S16: the boundary conditions of the plate are obtained.
S17: and obtaining an optimization design variable and an optimization target to obtain a shape optimization model.
S18: and solving the shape optimization model to obtain an optimal shape model with the optimal hole.
The embodiment of the invention can determine the size of the flat plate and the position of the circle center of the initial circular hole by establishing the initialized geometric model of the flat plate, then obtain the quantity value of the arc divided by the initial circular hole after generating the geometric middle model and the grid model of the flat plate, obtain the boundary condition, the optimized design variable and the optimized target for optimization, continuously adjust the radius of the arc divided by each section of the initial circular hole and the position of the circle center relative to the initial circular hole in the optimization process according to the boundary condition, the optimized design variable and the optimized target, finally determine the shape and the position of the optimal hole meeting the boundary condition and the optimized target to obtain the optimal shape model, and can rapidly and accurately design the flat plate with holes meeting the actual working requirements due to the optimization according to the boundary condition, the optimized design variable and the optimized target, thereby solving the problem that the traditional design method has long design period, the design efficiency is low.
Fig. 2 is a flow chart of another design method of a perforated flat plate, according to an embodiment of the present invention, for designing a circular hole on the flat plate, the circular hole being used for supporting a rotating shaft or a circular-section beam, as shown in fig. 2, the method includes:
s21: and acquiring design parameters of the flat plate.
Specifically, the design parameters include the size, shape, center of the initial circular hole, and radius of the initial circular hole of the flat panel.
Therefore, the size and the shape of the flat plate, the size of the initial circular hole and the position of the circle center of the initial circular hole on the flat plate can be determined according to design requirements, the sizes and the shapes of the flat plates with different purposes can be different, and the design requirements can include the space size of the position where the flat plate is installed and the connection mode of the flat plate and other structures.
S22: and generating an initialized geometric model according to the design parameters.
Fig. 3 is a schematic diagram illustrating an initialized geometric model of a flat plate according to an embodiment of the present invention, as shown in fig. 3, the initialized geometric model is a three-dimensional plate model, and the flat plate 10 includes an initial circular hole 10 a. Therefore, the contour shape of the flat plate can be obtained, a basic model is provided for subsequent design, and the geometric model is initialized to be a three-dimensional plate model.
S23: and extracting the middle plane of the initialized geometric model to obtain a geometric middle plane model.
Fig. 4 is a schematic diagram of a geometric midplane model, shown in fig. 4, in which the plate 20 includes an initial circular hole 20a, according to an embodiment of the invention.
Before a finite element method is adopted to generate a grid model, an initialized geometric model is required to be simplified, dimension reduction simplification is a common simplification mode, the dimension reduction simplification mainly comprises middle shaft transformation and middle surface simplification, the flat plate is a plate, the thickness of the flat plate is far smaller than the length and the width, the flat plate belongs to a thin-wall part, the middle surface simplification is suitable to be adopted, specifically, the middle surface of the plate in the initialized geometric model of the flat plate is extracted, the middle surface of the plate is a two-dimensional surface formed when the thickness of the plate is reduced to 0, and the extracted middle surface is the geometric middle surface model because the initialized geometric model only comprises one flat plate.
S24: and (4) dispersing the geometric mid-plane model by adopting a finite element method to obtain a grid model.
In this way, the geometric mid-plane model can be discretized into a plurality of associated units for analysis, that is, an infinite number of unknowns (flat plates) can be approximated by a finite number of unknowns (associated units) to obtain a more accurate simulation result.
Fig. 5 is a schematic diagram of a mesh model provided by an embodiment of the present invention, as shown in fig. 5, in which a flat plate 30 is discretized into a plurality of cells 31. The number of cells is determined by the cell size, and the smaller the cell size, the larger the number of cells, whereas the larger the cell size, the smaller the number of cells. It should be noted that the cell size may be manually set, and the larger the number of cells is, the higher the solving accuracy of the computer is, and accordingly, the lower the solving efficiency is, so the cell size may be set according to the actual requirement, which is not limited in the present invention.
S25: the numerical value of the arc into which the initial circular hole is divided is obtained.
Specifically, the number of arcs into which the initial circular hole is divided is 1, that is, the initial circular hole is not divided, and since the shape of the hole to be designed is a circle, only the radius of the hole needs to be optimized.
S26: and acquiring material properties and material thickness.
Specifically, the material properties at least comprise density, elastic modulus and Poisson's ratio, the thickness of the flat plate can be set to be 8-20 mm, specific numerical values can be set according to actual needs, and the material properties and the material thickness can be manually input according to the actual needs.
S27: the boundary conditions of the plate are obtained.
Specifically, the boundary conditions may include the degree of freedom of the flat plate and the maximum load borne by the flat plate, and for the flat plate in different working environments, the degree of freedom of the flat plate and the maximum load borne by the flat plate may be different, and the maximum load may be set according to an actual working condition, and the degree of freedom of the flat plate is also related to an actual installation form of the flat plate. Fig. 6 is a schematic diagram of a flat plate with a boundary condition applied thereto according to an embodiment of the present invention, where the flat plate 40 shown in fig. 6 is rectangular, and the first side 401, the second side 402 and the third side 403 of the flat plate 40 are all in a fixed state, so that the degree of freedom of the flat plate 40 is 0, the load applied is a downward pressure acting vertically on the wall of the hole, and the hole 41 is mainly used for supporting a beam or a rotating shaft with a circular cross section.
It should be noted that the maximum load applied should be greater than the load borne in the actual working condition, so as to improve the safety of the flat plate in the actual working condition.
S28: and obtaining an optimization design variable and an optimization target to obtain a shape optimization model.
Specifically, the optimization objective is set according to performance requirements including at least one of structural rigidity, structural strength, natural frequency, volume, and weight of the flat plate.
In this embodiment, the optimization design variable is the radius of the arc, the optimization goal is to maximize the structural rigidity, since the designed hole is used to support the rotating shaft or the circular-section beam, it is necessary to ensure that the shape of the hole is circular, and the size of the hole is changed by adjusting the radius of the arc, so as to maximize the structural rigidity of the flat plate.
In addition, the natural frequency closest to the target value can be used as an optimization target, and the target value can be artificially set according to specific working conditions, so that the difference between the natural frequency of the flat plate and the vibration frequency of the supported structure is maximum, and the flat plate can be ensured not to generate resonance in actual work.
S29: and solving the shape optimization model to obtain an optimal shape model with the optimal hole.
Fig. 7 is a schematic diagram of an optimal shape model according to an embodiment of the present invention, where a circular optimal hole 50a is formed in a flat plate 50, and the optimal hole in the flat plate is determined through a boundary condition, an optimization target, and an optimization design variable, so that the designed flat plate meets the requirement of an actual working condition, and thus the optimal shape model can be used as a finally obtained flat plate model to design and produce according to the flat plate model.
The steps S25 to S28 may be performed simultaneously.
Fig. 8 is a flow chart of another design method of a perforated flat plate according to an embodiment of the present invention, the method is used for designing a kidney-shaped hole on the flat plate, the kidney-shaped hole is used for reducing weight, as shown in fig. 7, the method includes:
s31: and acquiring design parameters of the flat plate.
Specifically, step S31 is the same as step S21, and is not described here.
S32: and generating an initialized geometric model according to the design parameters.
Specifically, step S32 is the same as step S22, and is not described here.
S33: and extracting the middle plane of the initialized geometric model to obtain a geometric middle plane model.
Specifically, step S33 is the same as step S23, and is not described here.
S34: and (4) dispersing the geometric mid-plane model by adopting a finite element method to obtain a grid model.
Specifically, step S34 is the same as step S24, and is not described here.
S35: the numerical value of the arc into which the initial circular hole is divided is obtained.
Fig. 9 is a schematic diagram of the initial circular hole divided into 4 arcs, and as shown in fig. 9, the circular hole in the flat plate 60 is divided into an arc 61, an arc 62, an arc 63, and an arc 64.
S36: and acquiring material properties and material thickness.
Specifically, step S36 is the same as step S26, and is not described here.
S37: the boundary conditions of the plate are obtained.
Fig. 10 is a schematic diagram of a flat plate with a boundary condition applied thereto according to an embodiment of the present invention, where the flat plate 70 shown in fig. 10 is rectangular, a first side 701 of the flat plate is fixed, and the flat plate receives a pulling force acting on a second side 702, where the pulling force is directed parallel to the plate surface and perpendicular to the second side 702.
It should be noted that the maximum load applied should be greater than the load borne in the actual working condition, so as to improve the safety of the flat plate in the actual working condition.
S38: and obtaining an optimization design variable and an optimization target to obtain a shape optimization model.
In this embodiment, the optimization design variables are the radius of the four-segment arc, the central angle of the four-segment arc, and the distance between the center of the four-segment arc and the position of the center of the initial circular hole, and the optimization target is that the flat plate has the lightest mass.
S39: and solving the shape optimization model to obtain an optimal shape model with the optimal hole.
Fig. 11 is a schematic diagram of an optimal shape model provided in an embodiment of the present invention, and the shape of the optimal hole 81 on the flat plate 80 is obtained as a kidney shape by solving the shape optimization model.
The steps S35 to S38 may be performed simultaneously.
FIG. 12 is a flow chart of a method for designing a perforated plate for use in designing a slotted hole in a plate for a support beam according to an embodiment of the present invention. As shown in fig. 12, the method includes:
s41: and acquiring design parameters of the flat plate.
Specifically, step S41 is the same as step S21, and is not described here.
S42: and generating an initialized geometric model according to the design parameters.
Specifically, step S42 is the same as step S22, and is not described here.
S43: and extracting the middle plane of the initialized geometric model to obtain a geometric middle plane model.
Specifically, step S43 is the same as step S23, and is not described here.
S44: and (4) dispersing the geometric mid-plane model by adopting a finite element method to obtain a grid model.
Specifically, step S44 is the same as step S24, and is not described here.
S45: the numerical value of the arc into which the initial circular hole is divided is obtained.
Fig. 13 is a schematic diagram of the initial circular hole divided into 4 arcs, and as shown in fig. 13, the initial circular hole on the flat plate 90 is divided into arcs 91, 92, 93, and 94.
S46: and acquiring material properties and material thickness.
Specifically, step S46 is the same as step S26, and is not described here.
S47: the boundary conditions of the plate are obtained.
Fig. 14 is a schematic diagram of another flat plate with boundary conditions applied thereto according to an embodiment of the present invention, where the flat plate 100 shown in fig. 14 is rectangular, and the first side 1001, the second side 1002, and the third side 1003 of the flat plate 100 are all in a fixed state, so that the degree of freedom of the flat plate 100 is 0, and the load applied is a downward pressure acting perpendicularly on the hole wall of the circular hole 101.
It should be noted that the maximum load applied should be greater than the load borne in the actual working condition, so as to improve the safety of the flat plate in the actual working condition.
S48: and obtaining an optimization design variable and an optimization target to obtain a shape optimization model.
In this embodiment, the optimization design variables are the radius of the four-segment arc, the central angle of the four-segment arc, and the distance between the center of the four-segment arc and the position of the center of the initial circular hole, and the optimization target is that the structural rigidity is the largest.
S49: and solving the shape optimization model to obtain an optimal shape model with the optimal hole.
Fig. 15 is a schematic diagram of an optimal shape model provided by an embodiment of the present invention, and an optimal hole 111 with a kidney shape is obtained on the flat plate 110 by solving the optimal shape model.
It should be noted that the above steps S45 to S48 may be performed simultaneously, and all or part of the steps of the above embodiment may be implemented by common design software, such as ANSYS (large general finite element analysis software developed by ANSYS corporation, usa), and the like.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (7)
1. A method of designing a perforated flat sheet, the method comprising:
constructing an initialized geometric model of the flat plate, wherein the initialized geometric model is provided with an initial round hole;
generating a geometric mid-plane model of the flat plate according to the initialized geometric model;
dispersing the geometric mid-plane model by adopting a finite element method to obtain a grid model;
acquiring the quantity value of the arc into which the initial round hole is divided;
acquiring material properties and material thickness;
acquiring the boundary condition of the flat plate;
obtaining optimization design variables and optimization targets to obtain a shape optimization model,
when a circular hole for supporting a rotating shaft or a circular-section beam is designed on the flat plate, the number of arcs into which the initial circular hole is divided is 1, the optimized design variable is the radius of the arcs,
when waist-shaped holes for weight reduction are designed on the flat plate, the number of arcs into which the initial circular hole is divided is 4, the optimized design variables are the radius of four segments of the arcs, the central angle of the four segments of the arcs and the distance from the centers of the four segments of the arcs to the position of the center of the initial circular hole,
when the waist-shaped hole for the support beam is designed on the flat plate, the number of arcs into which the initial circular hole is divided is 4, and the optimized design variables are the radius of four segments of the arcs, the central angle of the four segments of the arcs and the distance between the centers of the four segments of the arcs and the position of the center of the initial circular hole;
and solving the shape optimization model to obtain an optimal shape model with the optimal hole.
2. The method of claim 1, wherein the constructing an initialized geometric model of the plate comprises:
obtaining design parameters of the flat plate;
and generating the initialized geometric model according to the design parameters.
3. The method of claim 2, wherein the design parameters include a size, a shape, a center of the initial circular hole, and a radius of the initial circular hole of the flat sheet.
4. The method according to any one of claims 1 to 3, wherein the generating a geometric mid-plane model of the flat panel from the initialized geometric model comprises:
and extracting the middle surface of the initialized geometric model to obtain the geometric middle surface model.
5. The method of any one of claims 1 to 3, wherein the material properties include density, modulus of elasticity and Poisson's ratio.
6. A method according to any of claims 1 to 3, wherein the boundary conditions include the degree of freedom of the plate and the maximum load to be sustained.
7. A method according to any of claims 1 to 3, wherein the optimization objectives are set according to performance requirements including at least one of structural stiffness, structural strength, natural frequency, volume and weight of the flat sheet.
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